Determine the maximum bending moment, Mechanical Engineering

Determine the maximum bending moment:

A 12 m span simply supported beam is carrying a consistently distributed load of 2 kN/m over a length of 6 m from the left end and point loads 6 kN, 3 kN and 4 kN at distances of 7 m, 8 m and 9 m, respectively. Draw BM diagram and SF diagram for the beam and determine the maximum bending moment.

2454_Determine the maximum bending moment.png

Figure

Solution

Taking moments around A, and equating to zero.

RB × 12 - (4 × 9) - (3 × 8) - (6 × 7) - 2 × 6 ×(6/2)   = 0

Therefore,        RB = 11.5 kN, and

RA = (2 × 6) + 6 + 3 + 4 - RB = 25 - 11.5 = 13.5 kN

Shear Force (beginning from the left end)

 SF at A, FA = + 13.5 kN

SF at C, FC = + 13.5 - 2 × 6 = + 1.5 kN

SF just left of   D = + 1.5 kN

 SF just right of D = + 1.5 - 6 = - 4.5 kN

SF just left of  E = - 4.5 kN

SF just right of E = - 4.5 - 3 = - 7.5 kN

 SF just left of   F = - 7.5 kN

SF just right of F = - 7.5 - 4 = - 11.5 kN

SF just left of   B = - 11.5 kN = Reaction at B.

Bending Moment

BM at A, MA = 0

BM at C, M  = (13.5 × 6) - 2 × (6 ×(6/2))   = 45 kNm (considering left side)

BM at D, MD = (11.5× 5) - (4 × 2) - (3 × 1) = 46.5 kN m (considering right side)

BM at E,

ME = (11.5 × 4) - (4 × 1) = 42 kN m

BM at F,

MF = (11.5 × 3) = 34.5 kN m

The maximum bending moment take place at D where the shear force changes sign.

                       Mmax = 46.5 kN m.

Posted Date: 1/22/2013 12:44:01 AM | Location : United States







Related Discussions:- Determine the maximum bending moment, Assignment Help, Ask Question on Determine the maximum bending moment, Get Answer, Expert's Help, Determine the maximum bending moment Discussions

Write discussion on Determine the maximum bending moment
Your posts are moderated
Related Questions
STEP S FOR SOLVING PROBLEM FOR FINDING POWER: 1. Use formula stress (s) = force (Maximum Tension)/Area Where; Area = b.t that is, Tmax = σ.b.t 2. Unit mass (m) = r.b.t.

Draw bending moment diagram: Draw the shear force diagram (SFD) & bending moment diagram (BMD) for the beam illustrated in Figure . Solution Reaction at the support A,

define prandtl''s stress function

for an otto cycle, compression ratio=8.5:1,air inlet=15degree celsius and pressure=101.3kpa, maximum cycle temperature= 1800degree celsius, what is temperature after compression,te

Find the magnitude of the angular acceleration of system: A homogeneous sphere having a mass of 100 kg is associated to a slender rod having a mass of 20 kg. In the horizontal

Collapsible Soils and Subsidence There are soils which are quite stable when dry and they show large volume changes on wetting under load. Examples of  these soils are loess (w

Derive the mathematical expression for temperature distribution for plane wall with internal heat generation when both the surfaces are at same temperature?


Ceramics Ceramics are mostly inorganic crystalline materials characterized by high melting point and low ductility. Such materials are processed via methods other than melting